A directional instability criterion for surrounding rock of rectangular roadways driven by deviatoric stress gradient

Rectangular roadways in underground rock engineering frequently exhibit directional instability under non-uniform in-situ stress. Conventional criteria primarily focus on stress magnitude and plastic zone morphology, but fail to quantitatively characterize directional evolution induced by spatial stress heterogeneity. This study proposes a directional instability criterion based on the spatial gradient of the second invariant of deviatoric stress. A directionality index is constructed using gradient-weighted integration of high deviatoric stress regions to characterize the potential stress-field-driven instability tendency, while a plastic response index is defined from plastic zone propagation obtained via FLAC 3D simulations to represent the current deformation state, forming a coupled dual-indicator framework. A total of 40 numerical cases are analyzed under varying lateral pressure coefficients and height-to-width ratios. Results show that increasing lateral pressure shifts the high deviatoric stress regions from sidewalls toward roof and floor, accompanied by a transition in failure mode from sidewall-dominated to roof-and-floor-dominated instability. The directionality index is primarily governed by stress anisotropy, whereas the plastic response index is more sensitive to lithological heterogeneity. Based on the consistency maximization framework, the instability modes of surrounding rock are classified into four categories: sidewall instability, transitional instability, roof-and-floor instability, and inconsistent instability. Engineering validation in the 102-2 roadway of Jinneng Coal Mine confirms good consistency between predictions and field observations, and reveals asynchronism between stress-driven evolution and plastic response. Overall, the proposed criterion provides a quantitative framework for directional instability prediction by linking stress-field-driven tendency with the corresponding plastic deformation response.